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The emergence of Industry 4.0 has brought new concepts to the factories that optimize and improve conventional processes. These technologies have brought assignments to the industrial robots that allow them to perform tasks faster and more precisely. The improvement of the robot’s proprioception capacity and tactile sensitivity using sensors is a useful approach to achieve those goals. Optical fibers are a viable technology to be used as sensors in robotic devices because they are electrically passive and present electromagnetic immunity. This paper proposes a Fiber Bragg Grating (FBG) based sensing system to monitor robotic manipulators during their operation. It corresponds to smart textiles installed on the robot’s body to detect interactions with the environment. A mathematical model is proposed to find what should be the greatest distance between adjacent FBGs to detect contact at any point between them. From this, it is possible to obtain a minimum number of sensors to detect contact at any point and guarantee the highest spatial resolution of the system with lower costs. The tactile system is formed of a group of optical fibers with multiplexed FBGs embedded in silicone rubber. The optical fibers with the sensors are positioned between layers of polyethylene foam and cotton fabric. After the manufacturing process, temperature and force characterization were done on the sensors which make up the smart textiles. In the characterization results, almost all the FBG presented values of R² on the linear regression superior to 0.94. Individual analysis is performed for the sensors which present a low coefficient of determination. Finally, the system was tested in an experimental validation in which the robot was hit while executing a task. From the results, it can be observed that the system can provide the position on the robot’s body, the amplitude in terms of force and the instant of time in which an external impact occurred. published